第一篇：培優專項訓練八

培優專項訓練八

Unit 8 主題閱讀

閱讀理解

A

Zhao Hua is a student from a university.He has led a group of university student volunteers since last year.They help children at a primary school with their studies and daily lives.“ When I was a small child,” Zhao said, “ I knew March 5th was a day for people to learn from Lei Feng and help others, but I didn?t know the real meaning of the spirit of Lei Feng.Now when I see the smiling faces of the kids I have helped, I deeply understand Lei Feng.Helping others makes me happy.”Lei Feng（1940—1962）is one of the best-known soldiers in Chinese history.He lost his parents when he was very young.His neighbors brought him up.He died in an accident at the age of 22.He did manymoney to the parents of another soldier, and bought a ticket for a woman he didn?t know without telling her his name.On March 5th,1963, Chairman Mao called on people to “ Learn from Lei Feng” and made the day“Lei Feng Day”.Today almost 50 years has passed since Lei Feng?s death.Some people say that the spirit of Lei Feng is out.There have been many reports about the coldness(冷漠)of people towards strangers.This has made many Chinese people think deeply about themselves.Many people think we need to promote(提倡)that spirit again.The important thing is that we must be ready to help others and make it a habit.1.Which day is “Lei Feng Day”？

A.May 3 rd.B.May 5 th.C.March 3 rd.D.March 5 th.2.Who brought Lei Feng up?

A.His parents.B.Chairman Mao.C.His neighbors.D.Soldiers.3.The underlined phrase “good deeds” means _________ in Chinese.A.好人B.好事C.好夢D.好主意

4.Which of the following is NOT TRUE according to the passage?

A.Lei Feng gave his money to another soldier?s

parents.B.Lei Feng bought a ticket for a woman and he

told his name to her.C.Lei Feng always helped others.D.We should learn from Lei Feng.5.What?s the best title(標題)of this passage ?A.Lei Feng?s SpiritB.Lei Feng?s death

C.Lei Feng?s good neighborsD.University Student Volunteers

B

Like many people, I have no clear idea about heroes.At some point, we all wonder if we need a hero and what a hero really is.Although there are a lot of differences in cultures, heroes around the world generally share a number of characteristics(特點)which give us courage and make us want to learn from them.A hero does something worth talking about.A hero has a special story to tell and people think highly of it.But a hero is not just the person with great fame(聲譽).A hero has powers(力量)larger than himself.Some people want to live like a hero, and they have to experience life with a new and further meaning.A sure test for would-be heroes is what or whom they serve.What do they want to live and die for? If the answer suggests they serve only their own fame, they may be famous persons but not heroes.the power to move people.He creates new possibilities.Without Gandhi, India might still be part of Britain.Without Martin Luther King, Jr., Americans might take different buses, eat in different restaurants, go for walks in different parks, and shop in different stores because of the different colours of their skin.There might be changes in society without a hero, but the speed of change would be rather slow.Thanks to heroes in history, they make the society develop so rapidly.1.According to this passage, a hero is a person who always ________.A.gives us courage

B.thinks highly of othersC.shares great fame

D.stands on the mountaintop

2.If you want to live like a hero, you should _______.A.experience a new and meaningful lifeB.listen to something worth talking aboutC.serve your own fame and try to be famous D.know where and how you want to live and die 3.The underlined word “vision” in the passage means “__________”.A.風景B.想象C.遠見D.形象

4.Black people in America used to __________ before Martin Luther King, Jr..A.shop at the white?s storesB.drive buses with the whiteC.take walks in the white?s parksD.eat in restaurants without the white5.What can we learn from the passage?

A.We don?t need heroes anymore at some point now.B.Heroes are all the same though different in cultures.C.People get powers from heroes to move to a new place.D.Our society has developed faster because of heroes in history.綜合提升訓練

（八）I.單項選擇

1.This is ________interesting story and it is also ________ useful one.A.an;anB.an;theC.an;aD.a;a 2.I don?t like this one.Please show me ________ one.A.otherC.anotherA.Germen

B.the othersD.the other oneB.Germany

D.Germans

3.There are five ________over there.C.Germanys

4.I think you can do the work ________.A.yourselfB.myselfC.himselfD.your 5.The ________of the planes made us feel sick.A.voiceB.noiseC.soundD.smell 6.________ good health you have!

A.How aB.What aC.HowD.What

7.This plane is made ________ paper and it was made ________ my mother last night.A.of;byB.from;byC.with;forD.in;with

8.They all looked ________at the teacher and felt very ________.A.happy;happyC.happy;happily A.many

B.happily;happilyD.happily;happy C.littleD.a lot of

9.It was a dry year.We?ve had ________ rain.B.a few

10.Could you tell me when the meeting ________? A.beginB.beginsC.will beginD.beginning

11.I don?t know the school, but it?s ________ to be quite a good one.A.told B.spokenC.talkedD.said A.is finished

B.was finished

12.When your homework ________, you may go home.C.will be finishedD.has finished

13.When I looked into the room, I found Philip himself ________ in bed.A.lies

B.lyingC.lay

D.lie

14.The Wangs ________here for ten years.A.is livingB.have livedC.has livedD.lives

15.They ________the station ________the train started.A.won?t leave;until

B.not leave;untilD.left;until

C.didn?t leave;until II．完形填空

Ever since I was little, my favourite season was winter.I loved to play in the snow and enjoyed the hot chocolate.winter never gave me the special gift of snow on my birthday.I would ask my it didn?t snow on my birthday.She would laugh and tell me I asked too many questions.one day, she promised that she would make it snow on my next

birthday.That year, my birthday, my grandmother died.I was sad but angry because she had promised to make it snow.The day of my sixth birthday, I woke up and ran to the window, hoping to see just one snowflake(雪花).But there was no.I felt mad at my grandmother.She had broken a promise.By my sixteenth birthday, I , even though I still wished for it.During my party, I stayed with my friends and family and was truly Then I saw the white snow down all around.I was so excited that I ran around screaming and laughing.My friends all laughed me, but I didn?t care.When I home, my grandpa said he had a gift for me.I was given me a gift.It was a small white box, which looked old.I opened it.There was a crystal snowflake(冰晶雪花)with a card that , “Happy Birthday.”

How could this be? My grandpa said it was my grandmother?s final on my “sweet I was that my smiling grandmother angel was and had been watching over me.B.Unluckily

sixteenth”.I cried.16.A.Certainly

C.ImportantlyD.Luckily

17.A.whenB.howC.whetherD.why 18.A.ButB.OrC.Then19.A.onB.afterC.before21.A.had gotC.had found

D.So D.in

20.A.seasonB.snowC.breakfastD.winter

B.had madeD.had lost

D.feared

22.A.happyB.sadC.angryD.sorry 23.A.hadB.wasC.played24.A.fell

C.disappearingD.falling25.A.withB.atC.from

D.off

D.flew

26.A.arrived atB.reached atC.got

B.standing

27.A.excitedB.surprisedC.pleasedD.sad 28.A.wroteB.saidC.explainedD.appeared 29.A.orderB.mistakeC.wishD.decision 30.A.sureB.angryC.sadD.confident III.閱讀理解

Mrs.Blanches? husband went off on a business trip to America.He planned to leave New York for Washington.He wanted to catch the 4:00 pm plane to Washington.It was seven o?clock in the afternoon.Mrs.Blanches received a telephone call from her husband.He told her that he was still at the New York airport.Mrs.Blanches was so surprised and asked him what happened.“What happened, honey?” asked Mrs.Blanches.“Well,” said Mr.Blanches.“I really don?t know what happened, honey.Everything was going fine.At half past three, I got my air ticket, checked my luggage and waited in line at the gate.I walked across the runaway(飛機跑道)to the airport and on my way I saw one of my old friends.Have you

remembered him? His name is Jack Smith.Now Jack Smith is an engineer who works at the airport.I was excited that I shouted to him.I came up and wanted to shake hands with Jack.But a policeman ran to me quickly and caught me.”

“Why did he catch you?” Mrs.Blanches asked.“I don?t know,” said Mr.Blanches.All I said was“Hi,Jack!”

“Yeah, that is why they wouldn?t let you go,” said Mrs.Blanches.“They thought you were going to do harm to the whole plane.Only terrorists want to take control of a plane, and that is called ?

31.What was Mrs.Blanches? husband?s destination(目的地)? A.Washington, America.B.South America.C.New York.D.The New York airport.32.Where was Mr.Blanches when he called his wife? A.He was on the airport to Washington.B.He was still at the New York Airport.C.He was in Washington.D.He was on the railway station.33.Who was Jack Smith?

A.Mr.Blanches? new customer.B.Mr.Blanches? old customer.C.Mr.Blanches? brother.D.Mr.Blanches? friend.34.What does the underlined word mean in Chinese？

A.恐怖B.逮捕C.劫機 D.別動

35.Why did the policeman catch Mrs.Blanches? husband?

A.Because they thought he was going to do harm to the plane.B.Because they wanted to get his help in catching terrorists.C.Because they knew that he was a terrorist.D.Because Mrs.Blanches asked them to do so.IV．詞匯運用

36.Please help _______(你自己)to some fish, Tom.Don?t be so shy.37.Man can?t live ________(沒有)water, so we must make good use of it.38.Please listen to the speaker _________(仔細地)when he speaks.39.She is such a pleasant and _________(有幫助的)girl that we all like her.40.The foreign teachers in our school are from Germany.They are ________(德國人).V.句型轉換

對畫線部分 提問)

_________ _________ does a football match last?

42.The old lady was so tired that she couldn?t go any further.(改為簡單句)

The old lady was _________ _________ to go any further.43.Their new house is twice as big as the old one.(改為同義句)

Their new house is twice _______ ________of the old one.44.I wonder how I can get to the nearest underground station.（改為同義句）I wonder ________ _______get to the nearest underground station.45.If you do exercise a lot, you will be healthy.（改為同義句）

The ______ exercise you do, the _______ you will be.

第二篇：2013屆高三英語詞匯專項訓練(八)

2013屆高三英語詞匯專項訓練

（八）一、用所給單詞的適當形式完成句子

1.His inability to speak to English put him at a _________(advantage)at the international conference.2.Do you know anymore with a mental or physical _________(disabled)?

3.On Christmas Eve, we helped to put up the Christmas tree, the _______(decorate)and the balloons.4.With the __________(develop)of modern agriculture and industry, more waste has been produced.5.The coat is so ______(dirt)that I’ll take it to the cleaner’s.二、根據首字母或中文提示完成句子

1.The next day, Us President Franklin Roosevelt d_________ war against Japan.2.They worked from d__________ till dusk to meet the deadline.3.To what d__________ is he interested in playing computer games? 4.He turned a d__________ ear to our advice and now he is trouble.5.How excited they were!They d________ Class 5 in the football match and won the game yesterday.6.As usual, let’s have a __________(聽寫)of some English words and expressions.7.I’m terribly sorry, but didn’t do that ___________(故意地)

8.On our ___________(啟程，離開)from Tahiti, some of the crew took over the ship.9.The beauty of Guilin is beyond ____________(描述)

10.It’s hard to imagine how this quiet volcano _________(毀滅)the whole city.三、改寫同一句，每空一詞

1.The temple we visited last week has a history of thousands of years.The history of the temple that we visited last week can ____ _____ _____ thousands of years ago.2.When we are attacked, all of us will take up arms and fight to defend our country.When ________, all of us will take up arms and fight _______ _______ ________ country.3.My aunt Mary delivered a healthy and lovely girl this morning.My aunt Mary ____ _____ _____ a healthy and lovely girl this morning.4.The future of space research is dependent on how much money we have..The future of space research _______ _______ how much money we have.5.I’m sad that I can’t adapt to the climate here._____ _____ ______ , the climate here __________ ___________ me.四、選詞填空

1.They worked _______(deep, deeply)into the night, by which we are ______(deep, deeply)moved.2._______(Some day, The other day)I met him in the street and he told me that he would come to see me _______(some day, the other day).3.The police accused him of setting fire to the building but he _________(deny, refuse)having been in the area in the night of fire.五、選擇填空

1.The snake hasn’t bitten me yet, but I daren’t _____ to upset it.A.to do a thingB.do anythingC.to do somethingD.do nothing 2.____ the advances of science, the discomforts of the old age will no doubt always be with us.A.As forB.BesidesC.ExceptD.Despite 3.The policemen went into action _______ they heard the alarm.A.swiftlyB.presentlyC.quicklyD.directly 4.I saw the train leaving ______ the direction of Shanghai.A.in

B.to

C.withD.at 5.I can see a light _____ the distance, and I also see a strange _________ a distance of ten yards.A.in, inB.in, atC.at, inD.at, at 6.Her son, to whom she was so ________, went abroad for further education two years ago.A.loved

B.cared

C.devoted

D.affected 7.Over the past decades, sea ice ___ in the Arctic as a result of global warming.A.had decreasedB.decreasedC.has been decreasingD.is decreasing 8.The way he did it was different ________ we were used to.A.in whichB.in whatC.from whatD.from which 9.One of the best ways for people to keep fit is to ______ healthy eating habits.A.grow

B.develop

C.increase

D.raise六、一句多譯

1.我的外套和你的外套在顏色和款式方面不同，但尺碼相同

1)_________________________________________________________________2)_________________________________________________________________ 2.你能辨別金星（Venus）和其它的行星嗎？

1)_________________________________________________________________2)_________________________________________________________________ 3.令我非常高興的是，我通過了考試，拿到了駕照

1)_________________________________________________________________ 2)_________________________________________________________________ 4.我們發現他是個很難相處的人。

1)_________________________________________________________________2)_________________________________________________________________ 5.聽到考試沒及格的壞消息，他感到非常失望。

1)_________________________________________________________________2)_________________________________________________________________

第三篇：基礎知識訓練 八

基礎知識訓練 八

1、下列詞語中加點字的讀音完全正確的一組是（）

A．坯子（pī）稂莠（láng）裝模作樣（mú）少安毋躁（shāo）B．經幢（chuáng）標識（shí）扛鼎之作（gāng）拾級而上（shè）

C．褊狹（biǎn）掂量（liáng）呼天搶地（qiāng）疾風勁草（jìng）D．答應（dá）供職（gòng）強詞奪理（qiǎng）不著邊際（zhuó）

2、下列詞語中沒有錯別字的一組是（）A．辨證揣摩暮鼓晨鐘格物致知B．稟承 噩夢無事生非固步自封C．含蓋擔擱浮想聯篇若即若離D．告罄撤消顧名思義兵慌馬亂

3、依次填入下列各句橫線的詞語，最恰當的一組是（）

[1]因為還有別的事，經理不得不提前離去，他離開前一再我們要處理這起商品質量糾紛，一定要給消費者一個滿意的答復。

[2]由于交通事業的迅速發展，為城鄉物資交流提供了更為有利的條件。[3]這僅是你個人的觀點，而且論據不充分，不能別人接受。A．交待從而強制B．交代從而強迫C．交待進而強制D．交代進而強迫

4、下列各句中加點的成語使用恰當的一句是（）A．病菌雖說是微不足道的，但它對人的危害卻是非常嚴重的。

B．為了寫這篇文章，劉教授查找文獻，尋章摘句，做了上千張卡片，費了很多時間和精力C．人非圣賢，孰能無過？犯點小錯誤是在所難免的，也是不足為訓的，關鍵是要吸取教訓。D．金三角的販毒分子，在從境外獲得輕武器補充后，如虎添翼，制毒更加猖狂。

5、下列各句中沒有語病的一句是（）

A．經調查，劉曉慶及其所辦的兩個有限公司自1996年以來，采取不列、少列收入，多利支出，虛假申報，通知申報而拒不申報，偷逃稅款1458.3萬元。

B．在滴水成冰的冬季，筑路大軍冒著料峭的北風在工地上緊張地勞動著。

C．使用300電話卡不需要專用的電話機，如果能牢記自己的卡號和密碼您可以不必隨身攜帶300卡，因此它比磁卡和IC卡更加方便。

D．桐城派之所以“別樹一宗”并非由于清代文化政策或傳統勢力的支持影響，更重要的是因為它的理論的合理性。

6．下列各句中標點符號使用正確的一項是（）

A．這件事是讓你去做好呢？還是讓我去做好呢？B．你要不斷進步、識字、生產

C．張華考上北京大學，在化學系學習；李萍進了中等技術學校，讀機械制造專業；我在百貨公司當售貨員：我們都有光明的前途。

D．現代畫家徐悲鴻筆下的馬，正如有的評論家說的那樣，“形種兼備，充滿生機。”

基礎知識訓練 九

1、下列詞語中加點的字的讀音完全不相同的一組是（）A．甲醛蜷曲詮釋得魚忘筌權宜之計B．泥淖拙笨灼灼卓爾不群擢發難數C．懶怠瘌痢水獺春意闌珊天籟之音D．庇護秕谷臂膀篳路藍縷筆墨官司

2、下列句子中沒有錯別字的一句是（）

A．我們不能墨守成規，而要堅持科學研究先行，及時開發新的美容化裝產品。

B．至少有如下兩點足可令人三思：第一，文學創作和市場運作并非水火不相融；第二；文學創作絕對不是簡單的市場運作。

C．翻開書卷，構想那美麗的畫面，放縱自己的心隨主人公起起伏伏，想像主人公的音容笑貌，或遠隔時空與作者對話，咀嚼文字中的言外之意，弦外之音，這是一種何等的享受！D．他勸告那些不愿為公平競爭開綠燈的醫藥批發企業，如果還抱殘守缺，只會“為淵驅魚，為叢驅鵲”，最終將失去市場，無法生存。

3、依次填入下列各句橫線處的詞語，最恰當的一組是（）

[1]專家提醒消費者，購買商品房一定要注意，對于“”依據《合同法》相關規定，雙方有約定的按照約定執行；如果無約定，經營者違約時應雙倍返還，消費者違約時不予返還。[2]既然稱作“中學生新概念作文選”，就要編得中學生閱讀。

[3]來自中國銀監會的信息顯示，四大銀行的上市時間表基本排定，并以先海外、后國內的順序進行。

A．定金合適大概B．訂金合適大致C．定金適合大致D．訂金適合大概4下列各句中加點的成語使用恰當的一句是（）

A．一開盤，這只股票就一路狂跌，勢如破竹，使已經遭受股市重重打擊的股民又雪上加霜。B．我，15歲，一個中學三年級學生，在讀了許多報刊文學之后，心血來潮，見獵心喜，也學寫了一篇小說，冒失的向文學刊物投稿。

C．作者的這些散文，曾有十多篇在本報刊載過，因為受到許多讀者的喜愛，作者才連篇累牘地寫下去。

D．董事長，對您的好意，我只能敬謝不敏，因為我有自知之明，我做些具體的工作尚可，經理一職實難勝任。

5、下列各句中沒有語病的一句是（）

A．從古老的刀耕火種，到21世紀的現代化農副產品基地，悠長的歲月，教會了勤勞的松江人怎樣生活在這片土地上。

B．據了解，我市移動電話部門針對春節期間手機短信密集發送，對今年發送量進行了預測，并事先做好相關準備工作。

C．時下的店名和商品名在吸收外來詞時，追求時髦，嘩眾取寵，令人費解。這些叫人看不懂的名稱，只能讓人貽笑大方。

D．美國宇航局引以為豪的“勇氣”號火星車21日清晨突然發生故障，之后連續30小時不再向地面傳回任何有效信息，所有參與此項目的科學家全都各就各位晝夜不停地尋找解決故障的對策。

6、填入下列橫線處與上文銜接最恰當的一項是（）

這就是漢字，我的祖屋，我的家！我迷戀它雕梁畫棟的亭閣樓臺，我更迷戀它朝暉夕陰中隸楷行草的萬千氣象：

[1]賞心悅目的，是耀眼的光箭穿過寬闊而幽深的甬道，照亮祖屋的身軀，優雅而頎長；[2]心馳神曳的，是光線將祖屋分明的棱角隱去，只留輕盈身姿，飄飄欲飛；[3]令人陶醉的，是道道金輝，鋪撒祖屋的胸襟，舒展高貴，氣度雍容；[4]最最攝魂奪魄的，當是斑駁的樹影中，祖屋如龍蛇行走，曼妙莫測！

A．[1][2][3][4]B．[1][3][2]C．[2][4][1][3]D．[1][4][2][3]

第四篇：全等三角形培優專題訓練

做最適合你的數學培訓

八年級數學培優專題訓練

（二）探索三角形全等的條件

1、一張長方形紙片沿對角線剪開，得到兩張三角形紙片，再將這兩張紙片擺成如下圖形式，使點B、F、C、D

CA在同一條直線上.EAEP MN⑴求證：AB⊥ED；

⑵若PB＝BC，請找出圖中與此條件有關的一對全等三角形，并給予證明

2、如圖，在△ABC中，AC＝BC，∠ACB＝90°，AD平分∠BAC，BE⊥AD交AC的延長線于F，E為垂足，則結論：①AD＝BF；②CF＝CD；③AC＋CD＝AB；④BE＝CF；⑤BF＝2BE.其中正確的是（）

3、如圖，點C在線段AB上，DA ⊥AB，EB⊥AB，FC⊥AB，且DA＝BC，EB＝AC，FC＝AB，∠AFB＝51°，求∠DFC的度數.DFFBDBFCDBEDCAE

ACBF________________________________________________________________________________________________________________

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4、如圖，四邊形ABCD中，AB∥CD，AD∥BC，O為對角線AC的中點，過點O作一條直線分別與AB、CD交于點M、N，點E、F在直線M、N上，且OE＝OF.⑴圖中共有幾對全等三角形，請把它們都寫下來； ⑵求證：∠MAE＝∠NCF

AEBMONCDF5、在△ABC中，高所在直線AD和BE交于H點，且BH＝AC，則∠ABC＝_____________.6、下列三個判斷：

⑴有兩邊及其中一邊上的高對應相等的兩個三角形全等； ⑵有兩邊及第三邊上的高對應相等的兩個三角形全等； ⑶一邊及其它兩邊上的高對應相等的兩個三角形全等.上述判斷是否正確？若正確，說明理由；若不正確，請舉出反例.________________________________________________________________________________________________________________

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（三）全等三角形的應用

全等三角形常用來轉移線段和角，用它來證明：

①線段和角的等量關系 ②線段和角的和差倍分關系

③直線與直線的平行或垂直等位置關系

1、如圖，已知BD、CE分別是△ABC的邊AC和AB上的高，點P在BD的延長線上，BP＝AC，點Q在CE上，CQ＝AB.試判斷AP與AQ的關系，并證明.2、如圖，AD是△ABC的高，E為AC上一點，BE交AD于點F，且BF＝AC，FD＝CD，求證：BE⊥AC

FAADQPEBCE3、（2012〃阜新中考）如圖,在△ABC中,AB＝AC,AD＝AE,∠BAC＝∠DAC＝90°.⑴當點D在AC上時,如圖①,線段BD,CE有怎樣的數量和位置關系?證明你猜想的結論.⑵將圖①中的△ADE繞點A順時針旋轉α角(0°＜α＜90°)，如圖②，線段BD、CE有怎樣的數量關系和位置關系？問明理由.BEABDCDC①AEDBC②________________________________________________________________________________________________________________

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4、在△ABC中，AB＝AC，點D是直線 BC上一點（不與B、C重合），以AD為一邊在AD的右側作△ADE，使AD＝AE，∠DAE＝∠BAC，連接CE.⑴如圖①，當點D在線段BC上時，若∠BAC＝90°，則∠BCE＝_______度.⑵設∠BAC＝α，∠BCE＝β

a、如圖②，當點D在線段BC上移動時，α，β之間有怎樣的數量關系？請說明理由.b、當點D在直線BC上移動時，α，β之間有怎樣的數量關系？請直接寫出你的結論.BDAEBDC①AEC②________________________________________________________________________________________________________________

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（四）輔助線作法之連接法

在幾何證明中，常通過添加輔助線來構造全等三角形.常見的添加輔助線方法有：連接法、截長補短法、倍長中線法、翻折法、旋轉法以及利用特殊條件構造全等三角形等等.1、如圖，△ABC的兩條高BD，CE相交于點P，且PD＝PE.證明∶AC＝AB

2、已知AB＝DE，BC＝EF，∠B＝∠E，AF＝CD 求證：AC∥DF

3、如圖，AB交CD于點O，AD、CB的延長線相交于點E，且OA＝OC，EA＝EC.∠A＝∠C嗎？點O在∠AEC的平分線上嗎？

EBCDOABCDAFEAEBDPC________________________________________________________________________________________________________________

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（五）輔助線作法之倍長中線法

在題目條件中含有中線的問題，我們常用的輔助線就是將中線延長一倍，其目的是為了得一對全等三角形，將分散的條件集中到一個三角形中去.1、△ABC中，AB＝5，AC＝3，求中線AD的取值范圍.2、如圖，在△ABC中，AD是∠BAC的平分線，又是BC上的中線

求證：AB＝AC

3、（2014〃襄陽初三模擬）在△ABC中，D是邊BC上的一點，且CD＝AB，∠BAD＝∠BDA，AE是△ABD的中線.求證∶AC＝2AE

BEDCABDCAABDC________________________________________________________________________________________________________________

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AFE4、（競賽014）△ABC中，D為BC的中點，DE⊥DF交AB，AC于點E，F.求證：BE＋CF＞EF

6、（競賽015）例：已知AD是△ABC的中線，BE交AC于點E，交AD于點F，且AE＝EF.求證:AC＝BF

BDCAEFDBC________________________________________________________________________________________________________________

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（六）輔助線作法之截長補短法

截長法：在第三條線段上截下一段使其等于兩條線段中的一條，再證明剩余部分與另一條相等.補短法：把兩條線段中的一條補到另一條線段上去，證明所得新線段與第三條線段相等.1、已知AC∥BD，EA，EB分別平分∠CAB和∠DBA，點E在CD上.求證：AB＝AC＋BD

2、在四邊形ABCD中，AC平分∠BAD，CE⊥AB于點E，且AE＝?（AB＋AD）.求證∶∠B＋∠D＝180°

3、如圖，已知△ABC中，∠A＝90°，AB＝AC，D為AC的中點，AE⊥BD于E，延長AE交BC于F.求證：∠ADB＝∠CDF

________________________________________________________________________________________________________________

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4、如圖，∠C＝90°，AC＝BC，AD是∠BAC的角平分線.求證∶AC＋CD＝AB

12、如圖，已知AB＝CD＝AE＝BC＋DE＝2，∠ABC＝∠AED＝90°，求五邊形ABCDE的面積.CBABDCDAE________________________________________________________________________________________________________________

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（七）輔助線作法之利用特殊條件構造全等三角形

2、（2012〃“華羅庚杯”）如圖，在△ABC中，AC＝?AB，AD平分∠BAC，且AD＝BD 求證：CD⊥AC

ACBD________________________________________________________________________________________________________________

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（八）全等三角形在動態幾何中的運用

1、(競賽〃014〃3)如圖，△ABC的邊BC在直線l上，AC⊥BC，且AC＝BC.△EFP的邊FP也在直線l上，邊EF與邊AC重合，且EF＝FP.⑴在圖①中,請你通過觀察、測量、猜想并寫出AB與AP所滿足的數量關系和位置關系;⑵將△EFP沿直線l向左平移到圖②的位置時,EP交AC于點Q,連接AP,BQ.猜想并寫出BQ與AP所滿足的數量關系和位置關系,并證明你的猜想;⑶將△EFP沿直線l向左平移到圖③的位置時,EP的延長線交AC的延長線于點Q,連接AP,BQ.你認為⑵中所猜想的BQ與AP的數量關系和位置關系還成立嗎?若成立,給出證明;若不成立,請說明理由.A(E)EAEAQllBC(F)PFPBClBFCP Q________________________________________________________________________________________________________________

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（九）探究角平分線

一、知識清單

角平分線的定義：從一個角的頂點引出一條射線，把這個角分成兩個相等的角，這條射線叫做這個角的角平分線.三角形的角平分線定義：三角形的一個角的平分線與這個角的對邊相交，連結這個角的頂點和與對邊交點的線段叫做三角形的角平分線（也叫三角形的內角平分線）.由定義可知，三角形的角平分線是一條線段.角平分線性質:

1、角平分線上的點，到這個角的兩邊的距離相等.2、角平分線分得的兩個角相等，都等于該角的一半.3、三角形的三條角平分線交于一點，且到各邊的距離相等，這個點稱為內心.二、方法點撥

證明角平分線有兩種方法:一是運用定義證明兩個角相等;二是運用角平分線的判定方法.三、規律清單

①遇到角平分線,可從角平分線上的某一點向角的兩邊作垂線段(圖1).②遇到角平分線,?？衫梅鄯ɑ蚪亻L補短法解題(圖2).③有兩條角平分線(內角或外角)交于一點,則連接該點與三角形第三個頂點的線段會平分一個內角或外角(圖3).④有垂直于角平分線的線段,則延長這條線段以利用三線合一解題(圖4).⑤遇到角內的一點到角的兩邊有垂線段時,就連接這點與角的頂點,看能否平分已知角(圖5).⑥遇到有多條角平分線時,可嘗試用整體的思想解題(圖6).⑦有翻折條件時,除注意全等的結論,還應關注折線就是角平分線、是對稱軸（如圖7）.⑧角平分線、平行線、等腰三角形三個條件中出現任意兩個,?？芍苯拥玫搅硪粋€(如圖8）.AAACBDAFAEGDBDBC圖2B圖1CD圖3DCBC________________________________________________________________________________________________________________

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AA

CFEBDC圖4BFE

DECF圖5

ADBA1D2B3A1APFC'D'DAD2CB圖6EF?1＋?2＋?3＝90°?1＋?2＝90°－??BCBEC圖7B圖8CD

四、真題訓練

1、(2011〃鄂州〃競賽〃018 〃重慶中考）如圖，△ABC的外角∠ACD的平分線CP與內角∠ABC的平分線BP相交于點P，若∠BPC＝40°，則∠CAP＝_____________.BCDAP2、(競賽〃019)如圖，∠B＝∠C＝90°，M是BC的中點，DM平分∠ADC.求證:AM平分∠DAB

DCMAB________________________________________________________________________________________________________________

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3、(競賽〃019)如圖,在△ABC中,∠BAC＝90°,AB＝AC,BE平分∠ABC,CE⊥BE.AED1求證:CE＝ BD 2

BCA

4、如圖，在△ABC中，AD平分∠BAC，BD＝CD 求證：∠B＝∠C

5、如圖，在Rt△ABC中，∠C＝90°，AC＝BC，AD是∠BAC的平分線，交BC于D，DE⊥AB于E，若AB＝10cm，則△DBE的周長是多少？

ABDCAECDB6、（2011，恩施中考）AD是△ABC的角平分線，DF⊥AB，垂足為F，DE＝DG，△ADG和△AED的面積分別為50和39，則△EDF的面積為多少？

BEFGDC________________________________________________________________________________________________________________

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7、如圖，△ABC中，AD平分∠BAC，DG⊥BC且平分BC，DE⊥AB于E，DF⊥AC于F.求證：BE＝CF

8、在△ABC中，AD是∠BAC的平分線，E、F分別為AB、AC上的點，且∠EDF＋∠BAF＝180°

⑴求證：DE＝DF ⑵如果把最后一個條件改為AE＞AF，且∠AED＋∠AFD＝180°，那么結論還成立嗎？

9、如圖，已知AB＝AC，BE⊥AC于E，CF⊥AB于F，BE與CF交于點D 求證：點D在∠BAC的平分線上.10、如圖，在四邊形ABCD中，對角線AC平分∠BAD，AB＞AD，下列結論正確的是()A.AB－AD＞CB－CD B.AB－AD＝CB－CD C.AB－AD＜CB－CD D.AB－CD與CB－CD的大小關系不確定

BCAAEBGCFDAFEBDCBFDAECD________________________________________________________________________________________________________________

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11、（競賽014）如圖，已知△ABC中，∠B＝60°，∠BAC，∠BCA的平分線AD，CE相交于點O.求證：DC＋AE＝AC

12、(競賽〃019)如圖，已知△ABC，P為內角平分線AD、BE、CF的交點，過點P作PG⊥BC于G點。試說明∠BPD與∠CPG的大小關系，并說明理由。

BDGCAAEOBDCFPE________________________________________________________________________________________________________________

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（十）應用線段垂直平分線的性質和判定解題

一、知識清單

定義：經過線段中點并且垂直于這條線段的直線，叫做這條線段的垂直平分線。線段垂直平分線的性質：線段垂直平分線上的點與這條線段兩個端點的距離相等。線段垂直平分的判定：與一條線段兩個端點距離相等的點，在這條線段的垂直平分線上。

________________________________________________________________________________________________________________

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第五篇：培優班材料,平行四邊形專題訓練

特殊四邊形專題三：特殊四邊形中的探究問題

有關特殊四邊形中的探究問題是涉及特殊四邊形的幾何動態問題，要求學生自主探索、發現問題、總結規律，因此要求同學們對一些特殊四邊形的性質要掌握到位。解決此類問題的方法是先明確在變化過程中什么“不變”，特殊位置在什么地方，再從特殊到一般進行探究，這種方法在以后的數學學習中會經常用到。

【例1】已知：正方形ABCD中，∠MAN=45°，∠MAN繞點A順時針旋轉，它的兩邊分別交CB，DC（或它們的延長線）于點M，N，當∠MAN繞點A旋轉到BM=DN時（如圖1），易證MB+DN=MN。

（1）當∠MAN繞點A旋轉到BM≠DN時（如圖2），線段BM，DN和MN之間有怎樣的數量關系？寫出猜想，并加以證明；

（2）當∠MAN繞點A旋轉到如圖3所示的位置時，線段BM，DN和MN之間又有怎樣的數量關系？寫出你的猜想，并說明理由。

【例2】（1）操作發現：如圖1，在矩形ABCD中，E是BC的中點，將ABE沿AE折疊后得到AFE，點F在矩形ABCD內部，延長AF交CD于點G，猜想線段GF與GC有數量關系，并證明你的結論。

（2）類比探究，如圖2，將（1）中 的矩形ABCD改為平行四邊形，其他條件不變，（1）中的結論是否仍然成立？并說明理由。

【例3】如圖，正方形ABCD的角線AC，BD相交于點O。

（1）若E為AC上一點，過A作AGEB于G，AG，BD交于F，求證：OE=OF；

（2）若點E在AC的延長線上（如圖2），AGEB交EB的延長線于G，AG的延長線交直線BD于點F，其他條件不變，OE=OF還成立嗎？若成立，請給予證明；若不成立，請說明理由。